Update production server to Rhino 8 (from Rhino 7)

Background
We have had some troubles updating our Rhino.Compute server in the past and find the instructions on guide unclear regarding updating from major version 7 to 8 (and not just service release).
We are updating to rhino 8 to be able to use .NET 7 on our production server.

Question
We have Rhino.Compute 7 installed on the production server and wants to upgrade to Rhino.Compute 8, should we first install Compute 8 as well, and then run the upgrade scripts or will the upgrade script automatically upgrade from 7 to 8?

Maybe @AndyPayne knows?

What we have tried
We tried running the PowerShell command found on the section “Updating The Deployment” without success.

We managed to update the server to Rhino 8 using the following steps:

  1. Stop the application pool in the IIS service.
  2. Deleted the \inetpub\wwwroot\aspnet_client\system_web\4_0_30319\ directory (with the old installation of Rhino.Compute)
  3. Reran the Bootstrap script, step 1 again, but with Rhino 8.

Finally we had a problem with the IIS server responding with HTTP Error 503. The service is unavailable